# If = (a + ib), find the values of a and b.

Given:

Consider the given equation,

Now, we rationalize

[Here, we multiply and divide by the conjugate of 1 + i]

Using (a + b)(a – b) = (a2 – b2)

[ i2 = -1]

= (-i)100

= [(-i)4]25

= (i4)25

= (1)25

[ i4 = i2 × i2 = -1 × -1 = 1]

(a + ib) = 1 + 0i

On comparing both the sides, we get

a = 1 and b = 0

hence, the value of a is 1 and b is 0

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